What? Jefferson said this 10 years before the Constitution was written (if he indeed said it at all- please cite this quote) and he was certainly not referring to eligibility to be president.
Besides, his father was born in Kenya.
Rep. Bingham commenting on Section 1992 said it means “every human being born within the jurisdiction of the United States of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution itself, a natural born citizen.” (Cong. Globe, 39th, 1st Sess., 1291 (1866))
Bingham subscribed to the same view as most everyone in Congress at the time that in order to be born a citizen of the United States one must be born within the allegiance of the Nation. Bingham had explained that to be born within the allegiance of the United States the parents, or more precisely, the father, must not owe allegiance to some other foreign sovereignty (remember the U.S. abandoned England’s “natural allegiance” doctrine). This of course, explains why emphasis of not owing allegiance to anyone else was the affect of being subject to the jurisdiction of the United States.